Exercise 1: Download the dataframe pirate_survey_noerrors.txt from http://nathanieldphillips.com/wp-content/uploads/2015/05/pirate_survey_noerrors.txt. The data are stored in a tab-separated text file with headers. Load the dataframe into an object called pirates. Because it’s tab-separated, use sep = “”.

pirates <- read.table(
  file= "http://nathanieldphillips.com/wp-content/uploads/2015/05/pirate_survey_noerrors.txt", 
  header=T, 
  sep ="\t", 
  stringsAsFactors=F)
head(pirates)
##   id    sex headband age college tattoos tchests.found parrots.lifetime
## 1  1 female      yes  35   JSSFP      18             8                9
## 2  2   male      yes  21    CCCC       6             5                1
## 3  3 female      yes  27    CCCC      12             8                1
## 4  4   male      yes  19    CCCC       9             8                1
## 5  5   male      yes  31    CCCC      11             2               13
## 6  6   male      yes  21    CCCC       7             1                0
##   favorite.pirate sword.type  sword.speed
## 1      Blackbeard    cutlass 0.0638977084
## 2      Blackbeard    cutlass 0.5601675763
## 3        Anicetus    cutlass 0.0005400172
## 4    Jack Sparrow    cutlass 3.8770396912
## 5    Jack Sparrow    cutlass 0.5080594239
## 6    Jack Sparrow    cutlass 0.6248019344

Exercise 2 Conduct a one-sample t-test to test whether or not the mean age of pirates is significantly different from 25. What is the test statistic, p-value, and 95% confidence interval? (Note: access these directly from the object, don’t type them manually). What is your conclusion?

test.result <- t.test(x = pirates$age, mu = 25, alternative = "t")
test.result
## 
##  One Sample t-test
## 
## data:  pirates$age
## t = 14.5068, df = 999, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 25
## 95 percent confidence interval:
##  27.28634 28.00166
## sample estimates:
## mean of x 
##    27.644
mean(pirates$age)
## [1] 27.644
names(test.result)
## [1] "statistic"   "parameter"   "p.value"     "conf.int"    "estimate"   
## [6] "null.value"  "alternative" "method"      "data.name"
test.result$statistic
##       t 
## 14.5068
test.result$p.value
## [1] 2.044261e-43
test.result$conf.int
## [1] 27.28634 28.00166
## attr(,"conf.level")
## [1] 0.95

Conclusion: the mean age of pirates is significant different from 25

Exercise 3 Conduct a one-sample t-test to test whether or not the mean number of parrots owned by pirates is different from 2.7. What is the test statistic, p-value, and 95% confidence interval? (Note: access these directly from the object, don’t type them manually). Write the conclusion using APA style.

test.result.parrots <- t.test(x = pirates$parrots.lifetime, mu = 2.7, alternative = "t")
test.result.parrots
## 
##  One Sample t-test
## 
## data:  pirates$parrots.lifetime
## t = 0.7298, df = 999, p-value = 0.4657
## alternative hypothesis: true mean is not equal to 2.7
## 95 percent confidence interval:
##  2.586837 2.947163
## sample estimates:
## mean of x 
##     2.767
test.result.parrots$p.value
## [1] 0.4657048
test.result.parrots$statistic
##         t 
## 0.7297652
test.result.parrots$conf.int
## [1] 2.586837 2.947163
## attr(,"conf.level")
## [1] 0.95
test.result.parrots$parameter
##  df 
## 999

Conclusion: t(999) = 0.73, p = 0.47, 95% CI = [2.59, 2.95].

Exercise 4

A pirate from Captain Chunk’s Canon Crew (CCCC) claims that pirates from his college have faster sword speeds than pirates from Jack Sparrow’s School of Fashion and Piratry (JSSFP). Test this claim by conducting the appropriate (one-tailed!) two-sample test and report the result using APA format.

head(pirates)
##   id    sex headband age college tattoos tchests.found parrots.lifetime
## 1  1 female      yes  35   JSSFP      18             8                9
## 2  2   male      yes  21    CCCC       6             5                1
## 3  3 female      yes  27    CCCC      12             8                1
## 4  4   male      yes  19    CCCC       9             8                1
## 5  5   male      yes  31    CCCC      11             2               13
## 6  6   male      yes  21    CCCC       7             1                0
##   favorite.pirate sword.type  sword.speed
## 1      Blackbeard    cutlass 0.0638977084
## 2      Blackbeard    cutlass 0.5601675763
## 3        Anicetus    cutlass 0.0005400172
## 4    Jack Sparrow    cutlass 3.8770396912
## 5    Jack Sparrow    cutlass 0.5080594239
## 6    Jack Sparrow    cutlass 0.6248019344
speed.canoncrew <- subset(pirates, subset = college == "CCCC")$sword.speed
speed.canoncrew
##   [1] 5.601676e-01 5.400172e-04 3.877040e+00 5.080594e-01 6.248019e-01
##   [6] 3.754821e-01 1.939482e+00 2.427432e+00 1.542015e+00 1.113820e-01
##  [11] 1.330434e-01 1.049165e-01 5.576000e-01 4.460345e-01 1.998073e-01
##  [16] 7.021994e-01 8.829053e-01 2.114727e-02 1.549579e+00 6.926610e-01
##  [21] 4.971957e-01 2.417614e-01 7.008769e-01 2.241700e-01 8.925659e-02
##  [26] 1.045777e+00 8.497927e-02 1.788093e-01 7.068146e-01 7.896721e-01
##  [31] 5.152247e-01 3.165472e+00 4.805918e-01 9.999962e-01 1.783492e+00
##  [36] 1.947296e+00 4.898807e-02 2.698563e+00 3.116795e+00 5.511957e-01
##  [41] 9.074586e-01 8.903635e-01 1.148152e+00 2.332921e-01 8.336117e-01
##  [46] 1.418907e-01 2.743359e-01 1.078755e-01 8.104651e-01 8.149733e-03
##  [51] 1.843328e+00 7.305870e-01 4.194253e-01 2.369877e+00 1.118245e+00
##  [56] 6.380374e-01 1.183212e+00 2.329333e+00 4.374982e+00 4.469643e+00
##  [61] 4.381825e-01 6.589355e-03 2.581582e-02 1.208478e+00 2.585914e+00
##  [66] 5.716333e-01 2.545271e-01 1.506041e-01 7.298198e-01 3.649453e-01
##  [71] 2.894286e-01 4.560064e-01 1.077360e-01 2.007711e-01 1.470890e-01
##  [76] 1.189593e-01 5.218669e-02 1.018652e+00 8.128410e-01 6.928560e-02
##  [81] 1.637484e-01 2.943969e-01 2.906847e-01 7.653349e-01 2.602634e-01
##  [86] 9.358345e-01 6.186305e-01 3.205224e-01 1.854973e+00 2.425876e+00
##  [91] 4.502509e-01 1.638267e-01 2.204007e+00 8.272345e-01 7.198027e-01
##  [96] 5.363176e-01 2.876197e-01 1.297090e+00 2.937001e-01 3.247310e-01
## [101] 8.199752e-02 8.490938e-01 2.293795e-01 6.045739e-02 1.565931e+00
## [106] 1.287491e+00 8.871604e-01 2.229074e+00 1.119080e+00 3.688295e-01
## [111] 1.501998e+00 1.064032e-01 8.344286e-03 1.587497e+00 5.604504e-01
## [116] 2.651483e-01 1.568513e+01 1.099616e+00 1.280885e+00 4.022317e-01
## [121] 1.334544e-01 3.251940e-01 6.559079e-02 1.908560e+00 3.331757e-01
## [126] 1.007713e-01 3.469167e-01 2.171795e-01 1.347525e-01 2.203958e-01
## [131] 7.972324e-01 2.106336e-01 2.971572e-01 1.413101e+00 3.666174e+00
## [136] 9.556084e-01 4.434937e+00 5.772761e-01 4.013637e-01 2.365850e-01
## [141] 1.040930e+00 1.442629e-01 1.224632e-01 3.459428e-02 5.683983e-03
## [146] 4.211608e-01 5.585383e-01 1.922816e+00 2.815601e-01 4.713460e-01
## [151] 4.330847e-01 4.891439e+00 4.323803e-01 7.750247e-01 1.150696e-01
## [156] 4.279542e-02 1.516174e+00 4.245591e-01 1.853903e-01 3.688585e-02
## [161] 6.377197e-01 3.811051e-01 2.910501e-01 2.171130e+00 2.220635e-01
## [166] 1.626494e-01 1.732025e+00 3.312819e-01 6.194505e-01 3.025759e-01
## [171] 1.101694e-02 3.232476e-01 2.295802e-01 2.475035e+00 2.618120e-01
## [176] 1.341844e+00 2.070533e-01 4.602335e-01 3.963902e-01 8.800982e-01
## [181] 3.703059e-02 5.585638e+00 1.594193e-01 5.079449e-01 2.236681e+00
## [186] 4.497719e-01 1.124346e-01 5.063881e-01 1.979181e+00 8.313284e-01
## [191] 2.634013e-01 2.217553e-01 4.309932e-01 2.251215e-01 2.045582e-01
## [196] 8.616936e-02 1.305222e+00 4.078049e-02 1.089361e+00 7.460456e-01
## [201] 1.244320e+00 1.073097e+00 1.939204e+00 2.075483e-01 1.139250e-01
## [206] 2.218823e+00 2.138483e-01 1.937038e+00 6.199079e-01 1.368493e+00
## [211] 1.339832e-01 4.929589e-01 5.926497e-01 5.229909e-01 1.059918e+00
## [216] 3.783562e-01 1.629900e+00 4.117511e-02 2.192812e+00 3.766060e-01
## [221] 3.013055e-01 6.867009e-02 6.034146e-01 2.496650e-01 6.519737e-01
## [226] 7.267699e-02 1.104318e-01 5.163189e-01 9.611529e-01 6.074460e-03
## [231] 3.389507e-01 5.209594e-01 5.172579e-01 9.441635e-01 2.917065e+00
## [236] 3.926577e-01 1.362046e+00 1.659079e+00 9.199971e-01 1.984409e+00
## [241] 1.521718e+00 5.136742e+00 3.578960e-01 3.350474e+00 4.056691e+00
## [246] 5.561025e-01 9.861426e-01 1.111005e+00 2.771894e-01 6.497184e-01
## [251] 6.150954e-02 1.059676e-01 1.868502e-01 5.852235e-01 7.279339e-01
## [256] 1.463479e+00 7.144574e-02 2.505807e-01 4.822052e-01 6.747799e-01
## [261] 3.054914e-01 3.418094e-01 6.318649e-01 1.873142e-01 1.554926e+00
## [266] 1.732129e-02 1.961044e-01 9.053694e-02 1.165040e+00 1.497269e+00
## [271] 6.959624e-01 2.910337e-01 9.103463e-01 1.969896e+01 8.121839e-01
## [276] 1.985086e+00 2.914500e-01 2.186575e+00 9.506815e-02 4.739802e-01
## [281] 3.312458e-02 1.336813e-01 6.702066e-01 1.407475e+00 1.913901e-02
## [286] 8.461516e-01 1.315388e+00 1.413238e+00 7.401450e-01 4.560438e-01
## [291] 5.069209e-01 8.473268e-01 6.582849e-01 2.255082e-01 1.619147e-01
## [296] 1.961310e-01 5.678040e-02 6.696966e-01 5.620137e-01 9.790571e-02
## [301] 8.707838e-01 6.657598e-01 9.973127e-01 2.512308e+00 8.703731e-01
## [306] 8.675703e-02 1.224283e+00 1.258608e+00 7.100539e-01 5.442906e-01
## [311] 4.566566e-01 3.605781e-01 6.046085e-01 1.590077e+00 2.344497e-01
## [316] 1.143131e+00 4.263952e-01 1.837449e-01 4.410091e+00 2.612365e-01
## [321] 4.010497e+00 2.768050e-02 4.423285e-01 9.111589e-01 1.544809e+00
## [326] 3.141857e-02 7.012680e-01 1.628269e+00 4.823288e-01 1.369222e+00
## [331] 1.494556e-01 1.846474e-01 4.611318e-01 3.402446e-01 1.486768e+00
## [336] 1.325584e+01 9.075503e-01 1.093393e-01 6.571678e-02 5.626780e-01
## [341] 2.203999e+00 1.845760e-01 5.983962e-01 2.516358e+00 3.489807e-01
## [346] 1.176532e+00 6.716036e-01 2.070717e+00 7.577727e-01 8.285978e-02
## [351] 9.266372e-01 1.779547e-01 5.875600e-01 1.676608e+00 1.063221e+00
## [356] 6.802632e-01 1.139485e+00 4.878785e+00 9.383873e-01 4.855380e+00
## [361] 6.281072e-01 3.234269e-01 6.534266e-01 7.700885e-01 1.025747e+01
## [366] 5.485708e-01 8.633324e-01 1.094349e+00 1.448347e-01 1.996541e-01
## [371] 1.596386e-01 4.311112e-01 2.553268e-01 4.243214e-01 4.600624e-01
## [376] 5.653791e-01 4.797583e-01 1.250748e+00 1.390176e+01 2.172522e-01
## [381] 1.719787e-01 9.121918e-02 5.254634e-01 4.830451e-01 1.315224e+00
## [386] 6.639214e-01 1.329998e-01 5.686803e-02 7.230167e-01 6.429021e-02
## [391] 1.247632e+00 1.147107e+00 3.888407e-01 2.018595e-01 2.059213e-01
## [396] 1.207573e+00 4.090517e-01 2.262254e-01 1.654203e+00 3.682499e-01
## [401] 1.657695e+00 9.598890e-01 6.138907e-01 4.596730e-03 1.513471e+00
## [406] 1.124600e+00 8.933362e-01 2.568112e-01 1.914312e+00 1.364147e+01
## [411] 2.627199e-01 3.148103e-02 1.258724e-01 1.476152e-01 1.790729e+00
## [416] 9.205982e-01 1.169704e+00 8.980467e+00 5.400671e-01 1.467552e-01
## [421] 5.062859e-01 4.445175e-01 1.212032e-01 1.440071e+00 1.709612e-01
## [426] 4.330137e-01 6.677319e-01 7.032614e-01 5.930479e+00 9.399403e-01
## [431] 2.229484e-01 1.547071e+00 6.773974e-01 2.978832e-01 5.735309e-01
## [436] 6.542017e-01 1.175853e+00 3.724556e-01 4.033294e-01 1.385906e+00
## [441] 6.031382e-01 4.859671e+00 2.776726e-01 9.527666e-02 8.462945e-01
## [446] 1.754499e-02 1.935612e-01 1.672559e-01 8.722075e-04 9.105126e-01
## [451] 8.433278e-03 1.170261e+00 4.826847e-01 3.895827e-01 2.163192e-01
## [456] 3.786101e-01 6.193452e+00 3.266367e+00 5.061120e-01 3.068064e-03
## [461] 2.802201e-01 2.757569e-01 5.681105e-01 2.141354e-01 2.172576e-01
## [466] 9.982184e-01 9.069587e-01 2.129020e-01 6.536438e-01 5.740761e-01
## [471] 1.436881e+00 9.350353e-02 2.845830e-01 9.275341e-01 4.457242e+00
## [476] 2.820014e-02 7.133806e-01 1.245009e-01 2.073091e+00 1.060931e+00
## [481] 7.289050e-01 7.650413e-01 1.873399e-01 4.203098e-02 2.927887e-01
## [486] 6.665900e-01 1.238838e+00 1.733350e+00 2.631744e+00 2.118029e+00
## [491] 5.597690e-01 3.489115e-01 9.649745e-01 5.765052e-02 3.818936e-01
## [496] 9.460736e-02 1.538852e+00 1.578375e+00 2.610884e+00 1.957209e+00
## [501] 1.754579e+00 1.178596e+00 8.282815e-01 1.220814e+00 8.867583e-01
## [506] 3.718405e-02 1.153107e-01 7.512020e-01 1.266693e-01 1.078099e+00
## [511] 6.021759e-02 3.624644e-01 1.333664e-01 3.945935e+00 1.432365e+01
## [516] 1.325684e+00 4.660312e-01 5.901943e-01 8.599736e-02 4.105422e-01
## [521] 1.263343e+00 5.082279e-01 1.089339e+00 7.362130e-01 1.798725e+00
## [526] 5.777992e-01 6.488608e-01 3.882417e-02 6.770456e-01 5.375353e-01
## [531] 1.560301e-01 6.708608e-01 1.030149e+01 5.786194e-01 1.616277e+00
## [536] 4.577303e+00 4.400824e-01 2.354201e+00 4.842214e-01 4.519039e+00
## [541] 4.513842e-01 1.883830e+00 2.388598e-01 5.474742e-01 6.639975e-01
## [546] 1.304184e-01 7.008938e-01 8.132106e+00 4.204768e-01 2.219424e+00
## [551] 8.355997e-01 3.129891e-01 3.510254e-02 2.557273e-01 4.729540e-01
## [556] 1.077637e+00 7.997141e-01 2.037784e-01 4.488470e-01 4.354508e-02
## [561] 1.210671e+00 7.451408e-01 5.379743e-01 6.816289e-01 6.770447e-02
## [566] 2.555480e-01 1.274397e+00 4.028715e-01 1.798083e-01 4.866081e-01
## [571] 1.583797e+00 3.145840e+00 8.864684e-01 2.543515e+01 7.818817e-01
## [576] 5.075834e-01 2.246615e-01 8.469996e-01 3.444441e+00 1.131595e+00
## [581] 2.499325e-01 1.660780e+00 2.399925e-01 8.605341e-02 2.088768e-01
## [586] 1.366955e-01 4.676749e-01 1.351634e+00 4.187171e-01 1.750184e+00
## [591] 2.262278e-01 9.193301e-03 2.127289e+00 6.285478e-01 2.962818e-01
## [596] 1.027424e+00 3.438937e-01 2.959922e-01 4.262532e+00 5.396129e-01
## [601] 1.858013e+00 1.405947e-01 5.589299e-02 7.578077e-01 1.265808e+00
## [606] 4.505834e-01 3.284689e-01 4.946144e-01 2.292683e-01 6.087684e-02
## [611] 4.347086e-02 6.131719e-01 6.456086e-02 8.699685e-02 3.851591e-01
## [616] 1.207499e+00 7.995797e-01 2.163571e+00 7.809374e-01 3.370551e-01
## [621] 2.970853e-01 1.096394e-01 4.066580e-01 4.813544e-01 2.856105e-01
## [626] 2.310223e-01 1.368548e+00 1.803076e-01 2.574101e+00 4.174936e-01
## [631] 4.648978e-02 1.369773e+00 6.951140e-01 1.601687e+00 6.550617e-01
## [636] 1.063367e+00 6.748045e-01
speed.fashionandpiratry <- subset(pirates, subset = college == "JSSFP")$sword.speed

test.result.speed <- t.test(x = speed.canoncrew, y = speed.fashionandpiratry, alternative = "l")
test.result.speed
## 
##  Welch Two Sample t-test
## 
## data:  speed.canoncrew and speed.fashionandpiratry
## t = -1.4524, df = 540.345, p-value = 0.07348
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##        -Inf 0.03610759
## sample estimates:
## mean of x mean of y 
##  1.068027  1.336603
test.result.speed$statistic
##         t 
## -1.452414
test.result.speed$p.value
## [1] 0.07348343
test.result.speed$parameter
##       df 
## 540.3448
test.result.speed$conf.int
## [1]       -Inf 0.03610759
## attr(,"conf.level")
## [1] 0.95

t(540) = -1.45, p = 0.07, 95% CI [-Inf, 0.04]

Exercise 5

According to a recent blog post on Piratebook, pirates whose favorite pirate is Blackbeard have more tattoos than pirates whose favorite pirate is Jack Sparrow. Test this claim by conducting the appropriate test and reporting the result in APA format. Important! Do this test once using the t.test(x, y) notation, and once using the t.test(formula, data) notation.

fav.blackbeard <- subset(pirates, subset = favorite.pirate == "Blackbeard")$tattoos

fav.jacksparrow <- subset(pirates, subset = favorite.pirate == "Jack Sparrow")$tattoos

test.result.tattoos <- t.test(x = fav.blackbeard, y = fav.jacksparrow, alternative = "g")

test.result.tattoos
## 
##  Welch Two Sample t-test
## 
## data:  fav.blackbeard and fav.jacksparrow
## t = 0.0333, df = 137.3, p-value = 0.4867
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -0.6302564        Inf
## sample estimates:
## mean of x mean of y 
##  9.620000  9.607064
test.result.fav.pirate <- t.test(formula = tattoos ~ favorite.pirate,
subset = favorite.pirate %in% c("Blackbeard", "Jack Sparrow"),
data = pirates, alternative = "g")

test.result.fav.pirate
## 
##  Welch Two Sample t-test
## 
## data:  tattoos by favorite.pirate
## t = 0.0333, df = 137.3, p-value = 0.4867
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -0.6302564        Inf
## sample estimates:
##   mean in group Blackbeard mean in group Jack Sparrow 
##                   9.620000                   9.607064
test.result.fav.pirate$statistic
##          t 
## 0.03330627
test.result.fav.pirate$parameter
##       df 
## 137.3001
test.result.fav.pirate$p.value
## [1] 0.4867394
test.result.fav.pirate$conf.int
## [1] -0.6302564        Inf
## attr(,"conf.level")
## [1] 0.95

t(137) = 0.03, p = 0.49, 95% CI [-0.63, Inf]

Exercise 6

Is there a relationship between a pirate’s age and the number of treasure chests he/she’s found? Test this by conducting the appropriate test and report your results in APA format.

test.result.pirate.age <- cor.test(x = pirates$age,
y = pirates$tchests.found)

test.result.pirate.age
## 
##  Pearson's product-moment correlation
## 
## data:  pirates$age and pirates$tchests.found
## t = 2.8263, df = 998, p-value = 0.004802
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.02726784 0.15027323
## sample estimates:
##        cor 
## 0.08911029
test.result.pirate.age$statistic
##        t 
## 2.826339
test.result.pirate.age$parameter
##  df 
## 998
test.result.pirate.age$p.value
## [1] 0.004802335
test.result.pirate.age$conf.int
## [1] 0.02726784 0.15027323
## attr(,"conf.level")
## [1] 0.95

t(998) = 2.83, p < 0.01, 95% CI [0.03, 0.15], r=0.089

Exercise 7:

Repeat the previous test just for pirates who have owned less than 10 parrots and whose favorite pirate is Jack Sparrow. Report your results in APA format.

less.parrots <- subset(pirates, subset = parrots.lifetime < 10 & favorite.pirate == "Jack Sparrow")


test.result.less.parrots <- cor.test(x = less.parrots$age,
y = less.parrots$tchests.found)

test.result.less.parrots
## 
##  Pearson's product-moment correlation
## 
## data:  less.parrots$age and less.parrots$tchests.found
## t = 1.88, df = 437, p-value = 0.06077
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.004053305  0.181639084
## sample estimates:
##        cor 
## 0.08957122

t(437) = 1.88, p = 0.06, 95% CI [-0.00, 0.18], r=0.089

Exercise 8 Is there a relationship between the college a pirate went to and his favorite pirate? Test this by conducting the appropirate test and report your results in APA format

test.result.college <- with(pirates,
chisq.test(x = college,
y = favorite.pirate))

test.result.college
## 
##  Pearson's Chi-squared test
## 
## data:  college and favorite.pirate
## X-squared = 44.5956, df = 5, p-value = 1.753e-08

Conclusion: X-squared(5) = 44.59, p < 0.01